A frequently used device to measure the speed of bullets is the ballistic pendulum. It comprises of a heavy block of wood of mass M suspended by two long chords. A bullet of mass m is fired into the block horizontally. The block, with the bullet embedded in it, swings upwards. The centre of mass of the combination rises through a vertical distance h before coming to rest momentarily. In a particular experiment, a bullet of mass 40 gm is fired into a wooden block of mass 10 kg. The block is observed to rise by a height of 20.0 cm.

If the bullet penetrates the block to a depth of 3.0 cm, the approximate average force of resistance by the block of wood is

Options

A. `8.2xx10^(4)N`
B. `32.4xx10^(4)N`
C. `64.8xx10^(4)N`
D. `16.8xx10^(4)N`

Answer

D

Explanation

`v^(2)-u^(2)=2as`
`rArr 0-502^(2)=2xx a xx(3)/(100)`
`rArr a=-(502^(2)xx100)/(2xx3)~=4.2xx10^(8)m//s`
`vec(F)=vec(m)vec(a)=(40)/(1000)xx4.2xx10^(6)=16.8xx10^(4)N`
`therefore` (D)